Tuchel, 49, has replaced the sacked Julien Nagelsmann in charge of the six-time Champions League winners.
Nagelsmann lost his job at the German champions on Friday with the Bavarians second in the table but he had guided them to next month's quarter-finals in Europe's top-tier competition.
Tuchel, was fired from Chelsea in September despite guiding them to the 2021 Champions League and spoke to Bayern bosses late on Tuesday.
"Believe me or not, I was a bit dumbstruck in the first 30 seconds of our first discussion," Tuchel told reporters.
"I didn't know what we were talking about. It became clear that it was for right now.
"I was completely surprised. The timing was surprising. There was no contact beforehand," the former Paris Saint-Germain boss added.
Tuchel's first match will come as soon as April 1 after the ongoing international break.
Bayern will meet league leaders Borussia Dortmund, the club that Tuchel led from 2015-2017 before he left for PSG.
"It's the (big) match in German football," he said.
"It has another level of importance," he added.